Morse theory, Higgs fields, and Yang-Mills-Higgs functionals

Steven B. Bradlow, Graeme Wilkin

Research output: Contribution to journalArticlepeer-review


In this mostly expository paper we describe applications of Morse theory to moduli spaces of Higgs bundles. The moduli spaces are finite-dimensional analytic varieties but they arise as quotients of infinite-dimensional spaces. There are natural functions for Morse theory on both the infinite-dimensional spaces and the finite-dimensional quotients. The first comes from the Yang-Mills-Higgs energy, while the second is provided by the Hitchin function. After describing what Higgs bundles are, we explore these functions and how they may be used to extract topological information about the moduli spaces.

Original languageEnglish (US)
Pages (from-to)1-41
Number of pages41
JournalJournal of Fixed Point Theory and Applications
Issue number1
StatePublished - Mar 2012


  • Higgs bundles
  • Morse theory
  • surface groups

ASJC Scopus subject areas

  • Modeling and Simulation
  • Geometry and Topology
  • Applied Mathematics


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